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master's thesis
Modeli miješanih distribucija
Split: University of Split, Faculty of Science, 2024. urn:nbn:hr:166:811501
Zdilar, Gabriela
University of Split
Faculty of Science
Department of Mathematics

Institutional repository: Repository of Faculty of Science

Cite this document

Zdilar, G. (2024). Modeli miješanih distribucija (Master's thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:811501

Zdilar, Gabriela. "Modeli miješanih distribucija." Master's thesis, University of Split, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:166:811501

Zdilar, Gabriela. "Modeli miješanih distribucija." Master's thesis, University of Split, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:166:811501

Zdilar, G. (2024). 'Modeli miješanih distribucija', Master's thesis, University of Split, Faculty of Science, accessed 10 October 2024, https://urn.nsk.hr/urn:nbn:hr:166:811501

Zdilar G. Modeli miješanih distribucija [Master's thesis]. Split: University of Split, Faculty of Science; 2024 [cited 2024 October 10] Available at: https://urn.nsk.hr/urn:nbn:hr:166:811501

G. Zdilar, "Modeli miješanih distribucija", Master's thesis, University of Split, Faculty of Science, Split, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:166:811501

Metadata
TitleModeli miješanih distribucija
Title (english)Mixture Models
AuthorGabriela Zdilar
MentorSnježana Braić (mentor)
Committee memberSnježana Braić (predsjednik povjerenstva)
Committee memberAna Perišić (član povjerenstva)
Committee memberVesna Gotovac Đogaš (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Mathematics)
Split
Defense date and country2024-09-20, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Modeli miješanih distribucija dobro su poznat pojam u statistici u kojoj su se kroz povijest koristili za modeliranje heterogenosti populacije i generalizaciju pretpostavki distribucije. U novije vrijeme, ovi modeli također pružaju pogodan i formalan okvir za grupiranje i klasifikaciju, što su pojmovi usko vezani uz strojno učenje. Glavni cilj ovog rada je pregled modela miješanih distribucija, s posebnim naglaskom na Gaussov i Bernoullijev model miješanih distribucija. Čitatelj će biti detaljno upoznat s EM-algoritmom koji je ključan za procjenu parametara modela miješanih distribucija, a primijenit ćemo ga na spomenute Gaussove i Bernoullijeve modele te dati njegov općeniti oblik. Naposlijetku, EM-algoritam ćemo implementirati u RStudiju na raznim primjerima te analizirati dobivene rezultate.
Abstract (english)
Mixture models are a well-known concept in statistics, historically used for modeling population heterogeneity, generalizing distributional assumptions, and more recently, providing a convenient yet formal framework for clustering and classification—concepts closely tied to machine learning. The main objective of this paper is to review mixture models, with a special emphasis on the Gaussian and Bernoulli mixture models. Furthermore, the reader will be thoroughly introduced to the EM algorithm, which is crucial for estimating the parameters of mixture models. We will apply the EM algorithm to the aforementioned Gaussian and Bernoulli models and present its general form. Finally, the EM algorithm will be implemented in RStudio on various examples, and the obtained results will be analyzed.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:811501
Study programmeTitle: Mathematics; specializations in: specialization in Pure Mathematics, specialization in Computer Science, specialization in Education, specialization in Statistics and Computer Science
Course: specialization in Statistics and Computer Science
Study programme type: university
Study level: graduate
Academic / professional title: sveučilišni/a magistar/magistra matematike (sveučilišni/a magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-09-23 12:17:58